Lesson: Writing Equations of Lines

Comment on Writing Equations of Lines

Hi,
This is out of text but is there a way to find all co-ordinates that lies in this line
greenlight-admin's picture

You can use the equation of the line to find infinitely many points on the line.

For more on this, watch 2:15 to 2:50 of the following video lesson: https://www.greenlighttestprep.com/module/gre-algebra-and-equation-solvi...

Cheers,
Brent

greenlight-admin's picture

You can use the equation of the line to find infinitely many points on the line.

For more on this, watch 2:15 to 2:50 of the following video lesson: https://www.greenlighttestprep.com/module/gre-algebra-and-equation-solvi...

Cheers,
Brent

Why is the rise negative three and not just 3
greenlight-admin's picture

It all depend on which direction you travel from point to point.

If we move from the left-side point (-2, 4) to the right-side point (4, 1), then the run is +6 (since we're travelling in the direction in which the x-coordinate INCREASES), and the rise is -3 (since we're travelling in the direction in which the y-coordinate DECREASES)

If we move from the right-side point (4, 1) to the left-side point (-2, 4), then the run is -6 (since we're travelling in the direction in which the x-coordinate DECREASES), and the rise is +3 (since we're travelling in the direction in which the y-coordinate INCREASES)

In both cases, the slope is the same.

In the first case, the slope = rise/run = -3/6
In the second case, the slope = rise/run = 3/-6

Does that help?

Cheers,
Brent

Hi Brent, i read over the comment about being able to use the line to find any points, but i just want to make sure that when finding B aka the y-intercept (shown during 2:20 on the video lesson) we can just look at the graph and see that y intercept is 3, since it first touches the y axis at that y coordinate. Thanks
greenlight-admin's picture

Good question!
If a given graph clearly shows the y-intercept, then you need not calculate the y-intercept.
However, not all questions will be so kind :-(

Cheers,
Brent

Dear Brent
At this video (1.47min )is mentioned we could select either of point (4,1 ) or (-2,4) to the plugin in our equation it means we could choose any of them and no matter which one? Does this rule apply to all questions like this?
your reply is highly appreciated
Thanks
greenlight-admin's picture

That,s correct.
The only thing that matters is that, once you label one point as Point #1 and the other point as Point #2, you maintain that order when calculating the slope.

For example, let's say we want to find the slope of the line between points (5, 10) and (2, 6)
If we say that Point #1 is (5, 10) and Point #2 is (2, 6), then...
Slope = (y1 - y2)/(x1 - x2)
= (10 - 6)/(5 - 2)
= 4/3

Conversely, if we say that Point #1 is (2, 6) and Point #2 is (5, 10), then...
Slope = (y1 - y2)/(x1 - x2)
= (6 - 10)/(2 - 5)
= -4/-3
= 4/3

In both cases we get the same slope.

More on this here: https://www.greenlighttestprep.com/module/gre-algebra-and-equation-solvi...

Cheers,
Brent

In the xy-plane, triangular region R is bounded by the lines x = 0, y = 0, and 4x + 3y = 60. Which of the following points lie inside region R ?

Indicate all such points.

A. (2, 18)
B. (5, 12)
C. (10, 7)
D.(12, 3)
E. (15, 2)

It is highly appreciated if you could explain it in detail? How we should identify inequality ( 4x + 3y < 60)?
greenlight-admin's picture

I have provided a step-by-step solution here https://gre.myprepclub.com/forum/in-the-xy-plane-triangular-region-r-is-...

Have you had a chance to review that solution? If so, can you tell me what part(s) you would like me to elaborate on?

Cheers,
Brent

Hey Brent! Could you explain the problem from the official GRE book, Pg 123, #3. Really confused on how to approach the graph and how they got their answer.

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